\[ \boxed { \left ( ax+b \right ) x{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) + \left ( \alpha \,x+\beta \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) -f \left ( x \right ) =0} \]
Mathematica: cpu = 2.446811 (sec), leaf count = 40 \[ \text {DSolve}\left [x y^{(3)}(x) (a x+b)+(\alpha x+\beta ) y''(x)-f(x)+x y'(x)+y(x)=0,y(x),x\right ] \]
Maple: cpu = 0.468 (sec), leaf count = 1421 \[ \left \{ y \left ( x \right ) ={\it HeunC} \left ( 0,{\frac {-2\,b+\beta }{b}},{\frac { \left ( 2\,b+\beta \right ) a-\alpha \,b}{ab}},-{\frac {b }{{a}^{2}}},{\frac { \left ( 4\,a-\alpha \right ) {b}^{2}-\alpha \,\beta \,b+a{\beta }^{2}}{2\,a{b}^{2}}},-{\frac {ax}{b}} \right ) \left ( ax+b \right ) ^{{\frac { \left ( 2\,b+\beta \right ) a-\alpha \,b}{ab}}}{\it \_C3}+{\it HeunC} \left ( 0,{\frac {2\,b-\beta }{b}},{\frac { \left ( 2\, b+\beta \right ) a-\alpha \,b}{ab}},-{\frac {b}{{a}^{2}}},{\frac { \left ( 4\,a-\alpha \right ) {b}^{2}-\alpha \,\beta \,b+a{\beta }^{2}}{2\, a{b}^{2}}},-{\frac {ax}{b}} \right ) {x}^{{\frac {2\,b-\beta }{b}}} \left ( ax+b \right ) ^{{\frac { \left ( 2\,b+\beta \right ) a-\alpha \,b }{ab}}}{\it \_C2}+ \left ( ax+b \right ) ^{{\frac { \left ( 2\,b+\beta \right ) a-\alpha \,b}{ab}}}b \left ( -{x}^{{\frac {2\,b-\beta }{b}}} \int \!-{({\it \_C1}+\int \!f \left ( x \right ) \,{\rm d}x){\it HeunC} \left ( 0,{\frac {-2\,b+\beta }{b}},{\frac { \left ( 2\,b+\beta \right ) a-\alpha \,b}{ab}},-{\frac {b}{{a}^{2}}},{\frac { \left ( 4\,a-\alpha \right ) {b}^{2}-\alpha \,\beta \,b+a{\beta }^{2}}{2\,a{b}^{2}}},-{\frac {ax}{b}} \right ) \left ( ax+b \right ) ^{{\frac { \left ( -3\,b-\beta \right ) a+\alpha \,b}{ab}}}{x}^{{\frac {-2\,b+\beta }{b}}} \left ( \left ( \left ( 2\,b-\beta \right ) {\it HeunC} \left ( 0,{\frac {-2\,b+ \beta }{b}},{\frac { \left ( 2\,b+\beta \right ) a-\alpha \,b}{ab}},-{ \frac {b}{{a}^{2}}},{\frac { \left ( 4\,a-\alpha \right ) {b}^{2}-\alpha \,\beta \,b+a{\beta }^{2}}{2\,a{b}^{2}}},-{\frac {ax}{b}} \right ) +a{ \it HeunCPrime} \left ( 0,{\frac {-2\,b+\beta }{b}},{\frac { \left ( 2\,b +\beta \right ) a-\alpha \,b}{ab}},-{\frac {b}{{a}^{2}}},{\frac { \left ( 4\,a-\alpha \right ) {b}^{2}-\alpha \,\beta \,b+a{\beta }^{2}}{2\, a{b}^{2}}},-{\frac {ax}{b}} \right ) x \right ) {\it HeunC} \left ( 0,{ \frac {2\,b-\beta }{b}},{\frac { \left ( 2\,b+\beta \right ) a-\alpha \,b }{ab}},-{\frac {b}{{a}^{2}}},{\frac { \left ( 4\,a-\alpha \right ) {b}^{ 2}-\alpha \,\beta \,b+a{\beta }^{2}}{2\,a{b}^{2}}},-{\frac {ax}{b}} \right ) -{\it HeunC} \left ( 0,{\frac {-2\,b+\beta }{b}},{\frac { \left ( 2\,b+\beta \right ) a-\alpha \,b}{ab}},-{\frac {b}{{a}^{2}}},{ \frac { \left ( 4\,a-\alpha \right ) {b}^{2}-\alpha \,\beta \,b+a{\beta }^{ 2}}{2\,a{b}^{2}}},-{\frac {ax}{b}} \right ) {\it HeunCPrime} \left ( 0,{ \frac {2\,b-\beta }{b}},{\frac { \left ( 2\,b+\beta \right ) a-\alpha \,b }{ab}},-{\frac {b}{{a}^{2}}},{\frac { \left ( 4\,a-\alpha \right ) {b}^{ 2}-\alpha \,\beta \,b+a{\beta }^{2}}{2\,a{b}^{2}}},-{\frac {ax}{b}} \right ) xa \right ) ^{-1}}\,{\rm d}x{\it HeunC} \left ( 0,{\frac {2\,b- \beta }{b}},{\frac { \left ( 2\,b+\beta \right ) a-\alpha \,b}{ab}},-{ \frac {b}{{a}^{2}}},{\frac { \left ( 4\,a-\alpha \right ) {b}^{2}-\alpha \,\beta \,b+a{\beta }^{2}}{2\,a{b}^{2}}},-{\frac {ax}{b}} \right ) +{\it HeunC} \left ( 0,{\frac {-2\,b+\beta }{b}},{\frac { \left ( 2\,b+\beta \right ) a-\alpha \,b}{ab}},-{\frac {b}{{a}^{2}}},{\frac { \left ( 4\,a- \alpha \right ) {b}^{2}-\alpha \,\beta \,b+a{\beta }^{2}}{2\,a{b}^{2}}},-{ \frac {ax}{b}} \right ) \int \!-{({\it \_C1}+\int \!f \left ( x \right ) \,{\rm d}x){\it HeunC} \left ( 0,{\frac {2\,b-\beta }{b}},{\frac { \left ( 2\,b+\beta \right ) a-\alpha \,b}{ab}},-{\frac {b}{{a}^{2}}},{ \frac { \left ( 4\,a-\alpha \right ) {b}^{2}-\alpha \,\beta \,b+a{\beta }^{ 2}}{2\,a{b}^{2}}},-{\frac {ax}{b}} \right ) \left ( ax+b \right ) ^{{ \frac { \left ( -3\,b-\beta \right ) a+\alpha \,b}{ab}}} \left ( \left ( \left ( 2\,b-\beta \right ) {\it HeunC} \left ( 0,{\frac {-2\,b+\beta }{b }},{\frac { \left ( 2\,b+\beta \right ) a-\alpha \,b}{ab}},-{\frac {b}{{a }^{2}}},{\frac { \left ( 4\,a-\alpha \right ) {b}^{2}-\alpha \,\beta \,b+a {\beta }^{2}}{2\,a{b}^{2}}},-{\frac {ax}{b}} \right ) +a{\it HeunCPrime} \left ( 0,{\frac {-2\,b+\beta }{b}},{\frac { \left ( 2\,b+\beta \right ) a-\alpha \,b}{ab}},-{\frac {b}{{a}^{2}}},{\frac { \left ( 4\,a-\alpha \right ) {b}^{2}-\alpha \,\beta \,b+a{\beta }^{2}}{2\,a{b}^{2}}},-{\frac {ax}{b}} \right ) x \right ) {\it HeunC} \left ( 0,{\frac {2\,b-\beta }{b} },{\frac { \left ( 2\,b+\beta \right ) a-\alpha \,b}{ab}},-{\frac {b}{{a} ^{2}}},{\frac { \left ( 4\,a-\alpha \right ) {b}^{2}-\alpha \,\beta \,b+a{ \beta }^{2}}{2\,a{b}^{2}}},-{\frac {ax}{b}} \right ) -{\it HeunC} \left ( 0,{\frac {-2\,b+\beta }{b}},{\frac { \left ( 2\,b+\beta \right ) a-\alpha \,b}{ab}},-{\frac {b}{{a}^{2}}},{\frac { \left ( 4\,a-\alpha \right ) {b}^{2}-\alpha \,\beta \,b+a{\beta }^{2}}{2\,a{b}^{2}}},-{\frac {ax}{b}} \right ) {\it HeunCPrime} \left ( 0,{\frac {2\,b-\beta }{b}},{ \frac { \left ( 2\,b+\beta \right ) a-\alpha \,b}{ab}},-{\frac {b}{{a}^{2 }}},{\frac { \left ( 4\,a-\alpha \right ) {b}^{2}-\alpha \,\beta \,b+a{ \beta }^{2}}{2\,a{b}^{2}}},-{\frac {ax}{b}} \right ) xa \right ) ^{-1}} \,{\rm d}x \right ) \right \} \]